New complexity analysis for primal-dual interior-point methods for self-scaled optimization problems

Fixexd point theory and applications

Gue Myung Lee¹  Bo Kyung Choi¹ 

[1] Department of Applied Mathematics, Pukyong National University, Busan, Korea

关键词: Euclidean Jordan algebra;    self-scaled optimization problem;    primal-dual interior-point methods;    kernel function;    proximity function;    complexity analysis;    worst-case iteration bound;   

DOI  :  10.1186/1687-1812-2012-213

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

A linear optimization problem over a symmetric cone, defined in a Euclidean Jordan algebra and called a self-scaled optimization problem (SOP), is considered. We formulate an algorithm for a large-update primal-dual interior-point method (IPM) for the SOP by using a proximity function defined by a new kernel function, and we obtain the best known complexity results of the large-update IPM for the SOP by using the Euclidean Jordan algebra techniques. MSC:90C51, 90C25, 65K05.

【 授权许可】

CC BY